lay down simulation of viscoelastic fluids using the...

ICMF-2016 – 9th International Conference on Multiphase Flow May 22nd – 27th 2016, Firenze, ItalyICMF-2016 – 9th International Conference on Multiphase Flow May 22nd – 27th 2016, Firenze, ItalyICMF-2016 – 9th International Conference on Multiphase Flow May 22nd – 27th 2016, Firenze, Italy

Lay Down Simulation of Viscoelastic Fluids Using the Hybrid Immersed-Boundary Method

Andreas Mark1, Simon Ingelsten2 and Fredrik Edelvik3

Fraunhofer Chalmers Research CentreChalmers Science Park

SE-412 88 Göteborg

1 [email protected] [email protected] [email protected]

Abstract

Lay down of viscoelastic fluids is common in several manufacturing processes. In the automotive industry, sealing material is sprayedonto the vehicle body to prevent water leakage into cavities and to reduce noise. To predict the deposition and lower the environmentalimpact by reducing material consumption, a detailed physical understanding of the process is important. In this work the resultingsurface multi-phase flow is modeled and simulated in IBOFlow, the in-house multi-phase flow solver at the Fraunhofer-ChalmersCentre. In the solver the two phase flow is modelled by the volume of fluid method and the viscoelastic fluid by a general Carreurheology model. In the solver the scanned or CAD geometry is handled by the hybrid immersed boundary method and the materialinterface is resolved by the adaptive anisotropic octree grid. The resulting hanging octree and triangular nodes along the geometryare automatically handled by the immersed boundary method. To boost the computational performance the simulation domain is in anovel way dynamically divided into an active and an inactive part. The governing equations are only assembled and solved for in theactive part, which is determined by the local position of the injection nozzle. The interface between the active and the inactive cells arehandled by symmetry boundary conditions and the pressure is always set for a point inside the active domain. The sealing lay downsimulation is successfully validated for a number of real sealing beads on a plate and on a Volvo V40 vehicle. Finally, the importanceof resolving the nozzle in the simulation is investigated for a static case.

Keywords: immersed boundary method, sealing simulation, volume of fluid, rheology model, Carreau model

1. Introduction

Sealing material is applied to automotive bodies to coverholes and seams, where moisture otherwise might create a corro-sive environment. After the vehicle bodies are coated with electrocoat, the sealing material is applied by robots. In Figure 1 a num-ber of applied sealing beads are shown.

Figure 1: Flat bead sealing seams on a body-in-white.

As seen in the Figure the sealing beads are long (≈ 1m) andthin (≈ 3mm) and typically 50 meters of sealing material is ap-plied on a vehicle body. Further, the beads overlap and penetratesinto cavities and are applied in regions with complex geometry.

Hence, the application sets high demand on separation of scalesand the geometry handling. Further, the applied sealing mate-rial is shear thinning, that is the viscosity decays with increasingshear or force. Hence, a standard Newtonian viscosity model isnot sufficient and a more complex rheology model is required. Upuntil now the automotive industry has relied on individual expe-rience and physical validation for improving the complex sealingprocess.

However, with the increase in computational power modelingand simulation are integrated into the development of many othercomplex processes [3, 10]. By using simulations the risk and un-foreseen cost is reduced, and further optimization is performed inthe virtual prototyping stage. With virtual optimization the envi-ronmental impact and the lead time to develop new models arereduced. Further, automatic path planning of robot motions canreduce the cycle time or the number or required robots.

Not many researchers have tried to simulate the complex seal-ing process. In 2004 Domnick and Schneider [5] simulated theprocess with the commercial software Fluent. In their work thesealing material is modeled with the volume of fluid (VoF) mod-ule and a shear thinning rheology model is employed. With thisapproach the simulation times are very long, a boundary con-forming grid is required and the import of robot paths is notstreamlined. In 2011 Runqvist et al. [12] used smooth particlehydrodynamics (SPH) to simulate the sealing process. The La-grangian framework only considers one phase (the sealing mate-rial) and due to the high impact velocity the adaptive time step isvery low. However, the framework accurately captured the seal-ing lay down with a hollow cone applicator.

In this work, the in-house multi-phase flow solver IPS


IBOFlow [2] is employed to simulate the sealing process. The in-compressible Navier-Stokes equations are discretized on an adap-tive octree grid and the presence of all objects is handled by thehybrid immersed boundary method [7, 8]. Hence, moving objectsare handled with minimum overhead and the mesh generation isautomatic. The software also includes a very robust, novel VoFmodule, where the moving interface is dynamically refined. Tospeed up the simulations the simulation domain is in a novel waydynamically divided into an active and an inactive part.

IPS IBOFlow is integrated in the math-based software for vir-tual product and production realization, IPS [1]. In the IPS Vir-tual Paint Sealing software a detailed process simulation can becombined with sequence optimisation and motion planning to se-lect one solution for each seam and connect them by efficientmotions that minimise the cycle time. The structure of the rest ofthe paper is as follows: First the flow solver and rheology modelare described. Then the sealing simulation framework is summa-rized. In the result section, the sealing lay down simulation isvalidated for a number of beads on a plate and on a Volvo V40vehicle. To verify the approximate injection model, the resultsare compared to a resolved nozzle simulation for a static case.Finally the paper is summarized and conclusions are drawn.

2. Flow solver

An incompressible fluid is modeled by the Navier-Stokesequations,

∇ · ~u = 0 , (1)

ρf∂~u

∂t+ ρf~u · ∇~u = −∇p+ µ∇2~u+ ~s , (2)

where ~u is the fluid velocity, ρf is the fluid density, p is the pres-sure, µ is the apparent viscosity defined as the ratio between shearstress and shear rate, µ = σ

γ̇. ~s is the droplet source term includ-

ing the buoyancy force. The Navier-Stokes equations are dis-cretized with the finite volume method on a dynamic Cartesianoctree grid, which is automatically generated and allows adap-tive grid refinements to follow moving objects. The equationsare solved in a segregated way and the SIMPLEC method is usedto couple the pressure and the velocity fields [6]. All variablesare stored in a co-located arrangement and the pressure weightedflux interpolation is used to suppress pressure oscillations [11].The Backward Euler scheme is used for the temporal discretiza-tion and an adaptive fluid time step is employed such that themaximum Courant number based on the fluid velocity and themovement of the applicators are restricted.

The internal boundary conditions are handled by the hybridimmersed boundary method [8]. In the method the fluid veloc-ity is set to the local velocity of the object with an immersedboundary condition. Extrapolation and mirroring of the velocityclose to the boundary are used to formulate an implicit bound-ary condition which is added to the operator for the momentumequations. The mirroring results in a fictitious fluid velocity fieldinside the immersed object. Mass conservation is ensured by ex-cluding this velocity field in the discretized continuity equation.A thorough description of the method and an extensive validationcan be found in [8].

To boost the computational performance the simulation do-main is in a novel way divided into an active and an inactive part.The active part is defined by all cells laying closer than 5 cm fromthe sealing impact positions. Further, all injection cells need tobe connected with each other and cells that are not directly con-nected with an injection cell are made inactive (cells laying onthe opposite side of a scalar surface compared to the sealing noz-zle). The active region is updated every fifth time step. At everyupdate the active cells are given local indices that are mapped tothe global ones. The governing equations are only assembled andsolved for the active cells but the solution is stored on the full

grid. The interface between the active and the inactive cells arehandled by symmetry boundary conditions and the pressure is al-ways set for a cell inside the active domain. With this procedurethe amount of active computational cells does not increase whenthe simulated sealing bead becomes longer. Hence, the simula-tion time for the first second is in the same order of magnitude asthe final simulation second. Without this division the differencethe would be orders of magnitudes.

The two-phase flow in the sealing application is modeled withthe VoF method, where the local property of the fluid is depen-dent on the volume fraction. The volume fraction is transportedwith the local velocity field. To keep the interface between thesealing material and the air sharp a hybrid CICSAM convectivescheme is adopted [13].

The apparent viscosity of the adhesive is modelled accordingto the Carreau model [4],

µ = (µ0 − µ∞)(1.0 + (λγ̇)2

)0.5(N−1)(3)

where the apparent viscosity, µ, is dependent on the localshear rate, γ̇, λ and N are material constants derived from ex-periments. µ0 and ∞ are the zero-shear-rate viscosity and theinfinite-shear-rate viscosity, which represents the upper and lowerNewtonian plateaus defined as

limγ̇→0

σxyγ̇xy

= µ0 and limγ̇→∞

σxyγ̇xy

= µ∞. (4)

3. Sealing simulation framework

To perform a sealing lay down simulation, the described flowsolver is used with the VOF method to handle the multi-phaseflow and the Carreu fluid model to characterize the rheology ofthe material. The required input is a triangulation of the target ge-ometry, the robot motion of the sealing nozzle and a shear sweeprheometer test of the sealing material.

Due to the high Stoke’s number the flow pattern of the seal-ing material between the nozzle and impact is independent on theflow direction and velocity of the surrounding air. Furthermore,the short application distance implies that gravity has little or noeffect on the flow pattern in the air. But, when the material strikesthe target’s surface it begins to flow and the resulting depositionis highly dependent on the impact angle, material rheology, voly-metric flow and the target’s geometry. Therefore, in the air theflow dependent sealing spray pattern is reconstructed from exper-iments and the fluid flow solver simulates the multi-phase surfaceflow.

Figure 2: Top: Picture of the static spray pattern for three differ-ent volumetric flows (Red 10ml/s, green 15ml/s and orange20ml/s). Bottom: Simulated/reconstructed flow pattern for thedifferent volumetric flows visualized with virtual droplets.

The experimental spray pattern and the corresponding recon-struction for three different volumetric flows are shown in Fig. 2.


The reconstruction is based on ray tracing. The width of the spraypattern depends on both volumetric flow and distance from theapplicator, and is interpolated from the experimental data. Withthe help of the ray tracing the impact zone is determined and thevolymetric flow, angle and distance dependent impact pattern ispredicted with high accuracy. The similar for approach is alsoimplemented for the hollow cone nozzle, but is not presented inthis paper.

At the fluid cells corresponding to the impact positions closeto the target, the material is inserted as a volumetric materialsource in the fluid solver and the velocity is set by immersedboundary conditions in the momentum equations. To ensure theno-slip boundary condition on the surface of the target the hy-brid immersed boundary condition is adopted [8]. Furthermore,a reference pressure is set in the active fluid domain.

Table 1: Carreau parameters for the sealing materialParameter Value UnitZero-shear-rate viscosity, µ0 886.23 Pa · sInfinite-shear-rate viscosity, µ∞ 1.3418 Pa · sRelaxation time, λ 2.5510 sPower index, n -0.034 -

To determine the rheology of the sealing material used atVolvo Cars in Torslanda, tests are performed in a rotary rheometerwith a parallel disc. The shear sweep data is fitted to the Carreaurheology model with a least square method, see Table 1. Theresulting rheology model is shown in Fig. 3 together with exper-imental data. In the same test the material density is measured to1080 kg/m3.

Figure 3: The fitted Carreau model together with rheometer ex-periments.

Therefore, one time step in the sealing lay down simulationscan be summarized as:

1. Update position of applicators and target geometry

2. Calculate the adaptive fluid time step and update grid re-finements

3. Connect immersed boundaries with octree grid

4. Update and connect active cells

5. Solve the Navier-Stokes equations (1 - 2)

6. Inject and transport sealing material with the local velocity

7. Interpolate the material volume fraction to the octree nodes

8. Reconstruct the surface of the sealing material on the targetby a marching cube algorithm

9. Iterate

4. Results

In this section the sealing lay down simulation is validatedfor a number of beads on a plate and on a Volvo V40 vehicle.Finally, the importance of resolving the nozzle in the simulationis investigated for a static case.

To validate the simulation results obtained with the IPS Vir-tual Paint Sealing software, they are compared to measurementsfor four sealing beads applied to a plate with different processconditions and a production bead on a Volvo V40 vehicle. Forthe plates the volumetric flow, nozzle to plate distance (TCP dis-tance) and nozzle velocity are stated in Table 2. In Fig. 4 theexperimental and simulated beads are shown and in Fig. 5 theaverage bead widths are compared with excellent agreement.

Table 2: The experimental volumetric flow, nozzle to plate dis-tance (TCP distance) and nozzle velocity for the four validationbeads.

Bead number Volumetric flow TCP distance Velocity− ml/s mm mm/s1 30 35 4002 40 35 4003 50 35 4004 30 50 400

Figure 4: Top: The four experimental beads. Bottom: The corre-sponding simulated beads.


Figure 5: Comparison between the measured and simulated beadwidths.

The final verification is performed on a Volvo V40 vehicleproduced in the factory in Gent. An interesting bead in produc-tion on the internal left fender is chosen. In Fig. 6 the scannedexperimental bead (green) is compared with the simulated one(yellow). Notice the good agreement and how the material fillsthe corners like a ski slope.

Figure 6: Sealing bead verification on a Volvo V40 vehicle. Thescanned experimental bead is shown in transparent green and thesimulated bead in yellow.

To validate the projected nozzle simulation where the mate-rial is injected close to the target, a static nozzle simulation re-solving the material from the injector to the target is performed.The simulation case consists of a flat target and the applicatornozzle is located at 35mm distance. The spray direction isaligned with the normal direction of the target and the volumetricflow rate of sealing material is 15ml/s. In the projected noz-zle simulation the sealing material is injected at the target sur-face with a corresponding width and velocity of 14.7mm and

7.38m/s, respectively. A resolved nozzle simulation is also car-ried out where the flow of sealing material is simulated from theapplicator nozzle and through the air to its impact and flow onthe target surface. In Fig. 7 a resolved simulation is shown. Bothsimulations have the same resolution of the respective dynami-cally refined octree grids, where the smallest cubic cell side is0.25mm.

Figure 7: A resolved nozzle simulation, where the flow of thesealing material is simulated in the air and on the target. Top:The sealing material is shown together with the adaptive octreegrid. Bottom: The clipped sealing material is colored by the ap-parent viscosity in log scale.

In Fig. 8 the sealing mass resulting from the projected noz-zle simulation is shown at four different simulation times. Thecorresponding results from the resolved nozzle simulation maybe seen in Fig. 9. A slight difference in shape between the twosimulations exist. Mainly the difference is that in the resolvedsimulation a larger part of the sealing material flows and buildsup in the perpendicular direction to the flat bead as it hits the tar-


get. The same effect is not as significant in the projected nozzlesimulation. A slight difference between the results is reasonable,as in the projected nozzle simulation the material is injected withuniform velocity aligned with the normal direction of the targetsurface, and in the resolved simulation the resulting velocity pro-file is not uniform. Hence, the local shear rate differs at the impactposition and therefore also the resulting viscosity. Because, thephysics of the surface flow is dictated by the apparent viscositythe small deviations between the simulations are understood andreasonable.

Figure 8: Sealing material from the projected nozzle simulation.From left to right 0.6s, 0.10s, 0.20s and 0.40s.

Figure 9: Sealing material for the resolved nozzle simulation.From left to right 0.6s, 0.10s, 0.20s and 0.40s.

A more quantitative comparison of the sealing material fromthe two simulations is performed by comparing their width andthickness. The width in two directions are compared, namely inthe cross direction and the perpendicular direction with regardsto the orientation of the flat bead. The two orthogonal directionsare clarified in Fig. 10.

Figure 10: The two directions in which the width of the resultingsealing masses are measured in the flat plate case.

The cross width, the perpendicular width and the thickness ofthe sealing material produced by the two simulations are plottedagainst time in Fig. 11 to Fig. 13. The results are consistentwith the observation of similar sizes and similar growth pattern isfound for both simulations with regards to the three measures.The cross width, shown in Fig. 11, is larger in the projectedthan in the resolved nozzle simulation. The result is reasonablesince more material flows in the perpendicular direction, as dis-cussed above. The perpendicular width, shown in Fig. 12, isvery similar for the simulations for the larger part of the simula-tion time. A slightly smaller width is observed for the projectednozzle simulation for the latter part of simulation, which again isconsistent with the previous observations. Also the thickness inthe two simulations show very similar patterns, except it being

slightly larger in the projected nozzle simulation. The observa-tions clearly demonstrate that the projected nozzle simulation iscapable of producing results that to a good approximation pre-dicts the outcome of the resolved nozzle simulation. The aver-age differences between the simulations are 6.7% for the crosswidth, 1.9% for the perpendicular width and 8.7% for the thick-ness. From the relative small deviations, it is concluded that themost of the physics are modeled and simulated by reconstruct-ing the sealing material in the air and simulating the impact andsurface flow. Further, the projected nozzle simulation reduces thecomputational cost by orders of magnitude.

Figure 11: Cross width resulting from the projected and resolvednozzle simulation.

Figure 12: Perpendicular width resulting from the projected andresolved nozzle simulation.


Figure 13: Thickness resulting from the projected and resolvednozzle simulation.

5. Conclusions

From the plate and vehicle validation we conclude that theproposed framework is able to simulate the application of flatbead sealing spray in a reliable way. The projected and the re-solved nozzle simulation generate similar results, verifying thatthe projected nozzle simulation is sufficient to achieve good ac-curacy. Furthermore, the efficient implementation makes it possi-ble to simulate application of one meter of sealing material in lessthan an hour on a standard computer. This fact makes it possibleto include such detailed simulations in the production prepara-tion process and on-line programming of the sealing robots. Thiswork on virtual sealing is therefore an important step towards thevirtual paint factory and contributes to sustainable production byproviding simulation tools that can be used by the automotiveindustry to reduce the time required for introduction of new carmodels, reduce the cycle-time, reduce the environmental impactand increase quality.

6. Acknowledgments

This work was supported in part by the Sustainable Produc-tion Initiative and the Production Area of Advance at Chalmers.The support is gratefully acknowledged. The test geometries andexperimental data were provided by Volvo Car Corporation.

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lay down simulation of viscoelastic fluids using the...

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